and many more benefits!

GMAT Club Timer Informer

Hi GMATClubber!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Most Helpful Expert Reply

Re: Max has $125 consisting of bills each worth either $5 or $20
[#permalink]

Show Tags

08 Oct 2012, 01:53

3

5

SOLUTION

Max has $125 consisting of bills each worth either $5 or $20. How many bills worth $5 does Max have?

Let \(x\) be the # of 5$ bills and \(y\) the # of 20$ bills --> \(5x+20y=125\) --> \(x=?\)

(1) Max has fewer than 5 bills worth $5 each. \(x<5\) --> \(5x+20y=125\) --> \(y=\frac{125-5x}{20}=\frac{25-x}{4}\) as \(x<5\) and \(y\) must be an integer then only possible value for \(x\) is 1. Sufficient.

(2) Max has more than 5 bills worth $20 each. \(y>5\) --> \(5x+20y=125\) --> \(x=\frac{125-20y}{5}=25-4y\) as \(y>5\) and \(x\) must not negative then only possible value for \(y\) is 6, hence \(x=1\). Sufficient.

Most Helpful Community Reply

Re: Max has $125 consisting of bills each worth either $5 or $20
[#permalink]

Show Tags

08 Oct 2012, 04:07

6

2

SOURH7WK wrote:

Let x be $5 bill & y be $20 bill, 5x+20y =125, Find x?ST1: Sufficient: x<5, Therefore x can be 0,1,2,3,4. Here only x=1 satisfy the given equation and for all other value y will not be an integer value.ST2: Sufficient: y>5, y=6,7,8... Now for y =7 the total value exceeds 125. Therefore Y must be 6. And so x will be 1.

Hence Answer D.

A suggestion: always divide an equation by the GCD of the coefficients, it becomes easier to handle. In this case, 5x + 20y = 125, divide through by 5 and get:x + 4y = 25. Smaller numbers, positive integers...isn't it easier to see the solutions?

(1): Another approach would be to look at 25 as being a M4+1 (remainder 1 when divided by 4). 4y is divisible by 4, therefore x must leave a remainder of 1 when divided by 4. Since x is less than 5, the only possibility is x = 1. Just to practice divisibility properties...:O)(2): y > 5, then 4y > 20. Because 4*7 = 28 > 25, the only possible value for y is 6, and x must be 1.

General Discussion

Re: Max has $125 consisting of bills each worth either $5 or $20
[#permalink]

Show Tags

08 Oct 2012, 02:16

2

From stem 5x + 20y = 125Question is x=?Note :- x & y can take only integer values because we can not tear either $5 or $20 notes 1) x<5--> The only possible integer value is x=1 -->Sufficient2) y>5--> The only possible integer value is y=6 & x = 1 -->SufficientAnswer D
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: Max has $125 consisting of bills each worth either $5 or $20
[#permalink]

Show Tags

08 Oct 2012, 02:20

imo d...each alone is sufficientlet the number of bills of 5$ b x and bills for 20$ be ynow we have only two situations where 5x+20y=125either x=1 and y=6 --> (true wen we use statement 1)orx=5 and y=5 --> (true wen we use statement 2)

Re: Max has $125 consisting of bills each worth either $5 or $20
[#permalink]

Show Tags

08 Oct 2012, 02:23

1

Let x be $5 bill & y be $20 bill, 5x+20y =125, Find x?ST1: Sufficient: x<5, Therefore x can be 0,1,2,3,4. Here only x=1 satisfy the given equation and for all other value y will not be an integer value.ST2: Sufficient: y>5, y=6,7,8... Now for y =7 the total value exceeds 125. Therefore Y must be 6. And so x will be 1.

Hence Answer D.
_________________

RegardsSD-----------------------------Press Kudos if you like my post.Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

1) tells us that x < 5, so we try to maximize for 20 to control what possible values x can take. For y = 5 we have x = 5 and for y = 6 we have x = 1, no other combinations in that range are possible between X and Y. And since 1) makes it impossible for x = 5, x must be = 1.. So 1 is sufficient.

2) tells us that y > 5, so again we test if there are different possible values for y. For y = 6 we have x = 1.. And y can't actually be a higher value than 6 because then we break the restriction of 125 USD.. So clearly, y = 6 and x = 1, so 2 is sufficient.

Re: Max has $125 consisting of bills each worth either $5 or $20
[#permalink]

Show Tags

13 Dec 2017, 20:31

Hi All,

We're told that Max has $125 consisting of bills worth $5 or $20 each. We're asked for the number of $5 bills that Max has. Based on the 'restrictions' in this question, there are only a handful of possible ways to get to $125. As such, I'm going to list them out first (before we deal with the two Facts):

$125: Six 20s and one 5 Five 20s and five 5s Four 20s and nine 5s Three 20s and thirteen 5s Two 20s and seventeen 5s One 20 and twenty-one 5s Zero 20s and twenty-five 5s

1) Max has fewer than 5 bills worth $5 each.

With this Fact, there's only one possible option: Six 20s and one 5. Fact 1 is SUFFICIENT

2) Max has more than 5 bills worth $20 each.

With this Fact, there's only one possible option: Six 20s and one 5. Fact 2 is SUFFICIENT

Show Tags

Let \(x\) be the # of 5$ bills and \(y\) the # of 20$ bills --> \(5x+20y=125\) --> \(x=?\)

Any particular reason for not simplifying this to x+4y=25 before analyzing statements?Also we can use plugging approach since we know multiples of 5 and 20 and Sum = 125but it took me few extra sec to plug in values from 1 to 4 for x. (For constant value of y=1)
_________________